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ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 19 NO. 2

in industry. One significant source of limitation is the inef-

ficiency in the moderation process; the other lies in the

sources commercially available. The deflection focusing

positron gun (DFPG) developed at The University of Texas

addresses both of these limitations.

The DFPG has been designed to generate the most

intense source-based slow positron beams. Positrons

are created in a large ring of radioactive material. This

source geometry dramatically increases the number of

positrons generated by simply increasing the surface area

of the source that is contributing positrons to the beam.

Secondly, the DFPG uses advances in moderator geom-

etries to more efficiently produce moderated positrons.

The geometry of the DFPG also suppresses background

counts by greatly reducing the number of unmoderated

positrons leaving the gun.

POSITRON INTERACTIONS IN MATTER

Positrons are the antimatter partner of the electron.

The two particles have the same mass, but the positron

has an opposite charge. When slowpositrons—thosewith

less than a fewmegaelectron volts—encounter ametal or

semiconductor, three categories of outcomes are possible:

reflection, absorption and re-emission, and annihilation,

as depicted in Fig. 2.

A fraction of the positrons in a beamwill be scattered

elasticallywhen they encounter a surface. More positrons

are diffracted in this way when the beam energy is lower.

Measurement techniques such as low-energy positron

diffraction can use these diffracted positrons to develop

an interference pattern, which relays information about

the arrangement of the atoms at the surface of a metal or

semiconductor.

[6]

Positrons penetrate to an average depth that increases

with their initial kinetic energy. During this process, the

positrons undergo repeated inelastic deflections, losing

energy primarily through the creation of phonons and

plasmons. The implantation depths for a given positron

kinetic energy have a Makhovian profile.

[7]

An example

of implantation profiles for varying energies is shown in

Fig. 3.

Positrons lose energy via inelastic collisions until they

have thermalized with the material. Some may arrive at

a surface before they have fully thermalized; otherwise,

they diffuse through thematerial with an energy of

until

they annihilate with an electron or arrive at a surface.

Anumber of things canhappenwhenapositronarrives

at the surface. If the surface has a positive work function

greater than the positron’s energy, the positron may

become trapped there. If the positron has enough energy

to escape, it may be emitted as an epithermal positron,

or it may pick up an electron from the surface and escape

as neutral, atomlike positronium. If the positronic work

function

is negative, a thermalized positron may be

emittedwithan energy of

, allowing for the creation

of monoenergetic positron beams.

Positrons that do not end up back at the surface are

annihilated in the interior of the sample. Positrons in a

material have a diffusion length that is determined by the

material itself and its configuration. In a perfect crystal

lattice, this length is usually approximately 150 nm. Lattice

defects with regions of high local negative charge, such

as dislocations, vacancies, and near-certain impurities,

can trap positrons. In this case, their diffusion length is

diminished, but their lifetime is extended. Different types

of defects are associatedwith distinct lifetimes, which can

even be used to distinguish between different arrange-

ments of the same type of defect. For example, one can

determine if dopants tend to exist as single atoms, inpairs,

or in larger clusters, and in what ratios.

Positrons remaining in a sample eventually find an

electron and are annihilated. There are a number of

channels for this reaction to proceed down, but 99.7% of

the reactions result in the emission of two photons back-

to-back in the frame of the interaction. Each photon has

an energy very close to the mass energy of the electron

or positron: 511 keV. Because the electrons in the sample

are moving, there may be a difference between the refer-

ence frame of the interaction and that of the lab frame of

several electron volts. Tightly bound core-shell electrons

move much faster than outer-shell or conduction band

electrons and therefore showa greater difference fromthe

lab frame. This appears either as an increasing opening

angle when the moment difference is more transverse

to the direction of flight of the photons or as a greater

Fig. 3

Makhovian implantation profiles in single-crystal

silicon. Source: Ref 8